The U.S. received 124,000 H-1B visa petitions, 39,000 more than it can fulfill under two hiring caps, the government said Monday.

The U.S. Citizenship and Immigration Service held a computer-generated lottery on Sunday to distribute the visas, which can be used at the start of fiscal year 2014, beginning Oct. 1. With the lottery, a U.S.-based company that may be seeking only one or two H-1B visas is on the same footing as a large overseas-based offshore outsourcing firm that may have petitioned for thousands of temporary visas.

The U.S. has two caps, a 20,000-cap reserved for advanced-degree graduates of U.S. universities, and another 65,000 cap that includes no restrictions.

Advanced-degree holders who are applying under that exemption have an edge because that lottery is held first. Those not selected became part of the 65,000 limit.

The H-1B visas arrived in a rush. The government began accepting petitions April 1, and announced Friday that it had received enough to meet the cap.

The majority of H-1B visas go to large IT services firms, according to a Computerworld analysis of the data.

Separately, U.S. Sen. Chuck Grassley (R-Iowa) on Monday asked the immigration service (USCIS) to provide a breakdown on the number of women who received H-1B visas.

At a Senate Judiciary Committee hearing last month, of which Grassley is a member, Karen Panetta, a professor of electrical and computer engineering at Tufts University, said that the vast majority of H-1B visas are held by men. She was testifying for the IEEE-USA, where she served as director of the IEEE's Women in Engineering Committee.

The IEEE-USA has filed a Freedom of Information Act request with the USCIS requesting data on the number of women who received H-1B petitions, but has yet to get the data on an individual petition basis.

"Having the data is critical to understanding the problem and finding an answer," Grassley wrote in a letter to Janet Napolitano, the secretary of the Department of Homeland Security, which oversees USCIS. He asking for the data on women going back to 1992.

The last time the U.S. exceeded 85,000 visas within the first week was in 2008, when 163,000 petitions were received.